LEGO® stop-motion animations were developed to engage first-year university students in the topics of matrices, vectors, linear geometry and linear transformations. LEGO® provided a versatile medium through which a wide range of concrete and abstract concepts could be physically demonstrated in both two and three dimensions. It was also familiar…

Mechanical engineering students often find the formulation and analysis of dynamical systems difficult. The response of some mechanical engineering undergraduates is that as much as possible courses on mechanics are best avoided. The aim of this paper is to produce some interesting dynamical systems that may help to change the opinions of the…

In this paper, we pursue a materialist approach to tool use to account for the material dimensions of learning mathematics with technology while decentralizing the human body from activity. We root this vision in theoretical advances on embodied mathematics learning and tool use that have been recently offered as alternatives to traditional…

In recent years, teacher professional noticing has become more prevalent internationally. One common definition to distinguish professional noticing from everyday noticing includes the three interrelated skills of attending, interpreting and deciding to respond. We used qualitative analysis to explore prospective teachers' approximations of…

The purpose of this study is to investigate pre-service middle-level mathematics teachers' noticing of student mathematical thinking and teacher identity in the context of virtual professional experimentation performed through the Story"Circles" model. This study examined how pre-service middle-level mathematics teachers' education…

We began by observing a variety of properties related to the tangent and normal lines of three conic sections: a parabola, an ellipse, and a hyperbola. Some of these properties include specific relationships between the x- and y-intercepts of the tangent and normal lines. Using these properties, we were able to form several differential equations.…

Many approaches to make mathematics relevant to first-year engineering students have been described. These include teaching practical engineering applications, or a close collaboration between engineering and mathematics teaching staff on unit design and teaching. In this paper, we report on a novel approach where we gave higher year engineering…

In mathematic courses, construction of some concepts by the students in a meaningful way may be complicated. In such circumstances, to embody the concepts application of the required technologies may reinforce learning process. Onset of learning process over daily life events of the student's environment may lure their attention and may…

Computer graphics and animation experts have been using the Catmull-Rom smooth curve interpolation equations since 1974, but the vector and matrix equations can be derived and simplified using basic algebra, resulting in a simple set of linear equations with constant coefficients. A variety of uses of Catmull-Rom interpolation are demonstrated,…

LOGO and turtle graphics were an influential movement in primary school mathematics education in the 1980s and 1990s. Since then, technology has moved forward, both in terms of its sophistication and pedagogical potential; and learner experiences, preferences and ways of thinking have changed dramatically. Based on the authors' previous work and a…

This study mainly aims to develop an effective strategy to overcome the known difficulties in teaching negative numbers. Another aim is to measure the success of this teaching strategy among a group of elementary level pupils in Izmir, Turkey. Learning negative concepts are supported by computer animations. The academic achievement test developed…

Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…

Macromedia's FLASH development system can be a great tool for mathematics education. This article presents detailed Flash tutorials that were developed and taught by the author to a group of mathematics professors in a summer course in 2005. The objective was to educate the teachers in the techniques of animating equations and mathematical…

This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of 'cart-pendulum' electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts…

A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…